Upload an image of your drawings.   One of the intermediates in the biosynthesis of epinephrine is the amino acid L-dopa, which has two phenolic OH groups at the 3 and 4 positions of the benzene ring of Phe. Following the PLP mediated decarboxylation of L-dopa, the side chain alkyl group is hydroxylated to form the hormone norepinephrine. The final step in the biosynthesis of epinephrine is N-methylation of norepinephrine to form epinephrine by SAMe (S-adenosy methionine). Outline the series of reactions that would take a carbon atom from either Ser or Gly and deliver it as a methyl group to norepinephrine to form epinephrine. Show all necessary cofactors. You may use names, structures, or acceptable abbreviations. (4 pts.) Following the transfer of a methyl group, SAMe is converted to homocysteine. High levels of homocysteine in the blood have been correlated with coronary heart disease, stroke, atherosclerosis, neural tube defects, and dementia in the elderly. Homocysteine can react with Ser with the loss of water to form cystathionine. Cystathionine is cleaved to form Cys and α-ketobutyrate in a PLP dependent reaction. Show the series of reactions that converts 

A 20-year-old man was stabbed in the chest with a jackknife (pocket knife) with a blade five centimeters long. The stab wound in the left fourth intercostal space was approximately two centimeters lateral to the body of the sternum. What chamber of the heart would likely be injured?

According to new research, the AKAP11 gene was identified as a risk factor for what disease?  (1 point) New research studying frogs have found that their claws evolved into what human trait? For an additional point, what gene family did it arise from?  (2 points max) Why is the discovery of consistent DNA twisting by SMC proteins across different organisms significant from an evolutionary perspective? (2 points max) Select one biology topic that was covered in the course that you didn’t know about before (and surprised you). What was it? What did you learn and how will it affect you as you progress on your life journey? HAVE A FANTASTIC BREAK AND BEST OF LUCK IN YOUR FUTURE COURSES/CAREERS! Please take a few minutes and fill out the Course Survey that is in the newest Announcement; it helps me shape future classes. 

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The matrix  

 Use Laplace transforms to solve the IVP:

Answer parts (a)(b)(c): (a): Find all constant (equilibrium) solutions to the following ODE (if there are none, write “none”):

 Suppose  the position (measured in meters) of a  mass on a spring, x(t),  is modeled by the ODE:  . When x(t)>0 the spring is stretched, and the spring is compressed when x(t). Answer parts (a)(b)(c) a)  Solve for  the position of the mass x(t) b)  How far does the mass get from the equilibrium position? c) Keeping the initial position at x(0) = 0, what initial velocity would you have to give in order to make the mass get exactly 10 meters away from the equilibrium position before it turns around and heads back to the equilibrium position? That is, you need to determine what x'(0) needs to be to achieve this.  Hint: you first need to determine how the amplitude depends on x'(0).